Select The Best Answer For The Question.A Triangle-shaped Machine Part Has Sides Of $ 2 \frac{1}{2}\$} Inches, ${ 3 \frac{1}{4}\$} Inches, And 5 Inches. The Triangle's Perimeter Is A. ${$11 \frac{1 {2}$}$ Inches.B. [$10
Introduction
In geometry, the perimeter of a triangle is the sum of the lengths of its three sides. When dealing with mixed numbers, it's essential to convert them to improper fractions to simplify calculations. In this article, we'll explore how to calculate the perimeter of a triangle with sides of mixed numbers and provide a step-by-step solution to the given problem.
Understanding Mixed Numbers
Before we dive into the problem, let's review what mixed numbers are. A mixed number is a combination of a whole number and a fraction. For example, [\frac{5}{2}$]. To add or subtract mixed numbers, we need to convert them to improper fractions.
Converting Mixed Numbers to Improper Fractions
To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator. The result is then written as an improper fraction.
- [\frac{(2 \times 2) + 1}{2}$] = [$\frac{5}{2}$]
- [\frac{(3 \times 4) + 1}{4}$] = [$\frac{13}{4}$]
Calculating the Perimeter of the Triangle
Now that we have converted the mixed numbers to improper fractions, we can calculate the perimeter of the triangle.
The perimeter of a triangle is the sum of the lengths of its three sides. In this case, the sides are [\frac{13}{4}$] inches, and 5 inches.
To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 2 and 4 is 4. So, we can rewrite the fractions with a common denominator of 4.
- [\frac{5 \times 2}{2 \times 2}$] = [$\frac{10}{4}$]
- [\frac{13}{4}$]
Now we can add the fractions:
[\frac{13}{4}$] + 5 = [\frac{43}{4}$]
To convert this improper fraction back to a mixed number, we divide the numerator by the denominator:
[$\frac{43}{4}$ = [$10 \frac{3}{4}$]
Conclusion
In conclusion, the perimeter of the triangle is [$10 \frac{3}{4}$] inches. This is the sum of the lengths of its three sides, which are [$2 \frac{1}{2}$] inches, [$3 \frac{1}{4}$] inches, and 5 inches.
Answer
The correct answer is:
- B. [$10 \frac{3}{4}$] inches
Additional Tips and Resources
- When dealing with mixed numbers, it's essential to convert them to improper fractions to simplify calculations.
- To add or subtract mixed numbers, we need to convert them to improper fractions.
- The perimeter of a triangle is the sum of the lengths of its three sides.
- To calculate the perimeter of a triangle, we need to find a common denominator for the fractions and add them.
References
- Math Open Reference: A comprehensive online reference for mathematics.
- Khan Academy: A free online platform for learning mathematics and other subjects.
Frequently Asked Questions
- Q: What is the perimeter of a triangle?
- A: The perimeter of a triangle is the sum of the lengths of its three sides.
- Q: How do I calculate the perimeter of a triangle with mixed numbers?
- A: To calculate the perimeter of a triangle with mixed numbers, we need to convert them to improper fractions and add them.
Related Topics
- Geometry: The branch of mathematics that deals with the study of shapes and their properties.
- Perimeter: The distance around a shape.
- Mixed Numbers: A combination of a whole number and a fraction.
Frequently Asked Questions: Calculating the Perimeter of a Triangle ====================================================================
Q: What is the perimeter of a triangle?
A: The perimeter of a triangle is the sum of the lengths of its three sides.
Q: How do I calculate the perimeter of a triangle with mixed numbers?
A: To calculate the perimeter of a triangle with mixed numbers, you need to convert them to improper fractions and add them. Here's a step-by-step guide:
- Convert the mixed numbers to improper fractions.
- Find a common denominator for the fractions.
- Add the fractions.
- Convert the result back to a mixed number.
Q: What is the formula for calculating the perimeter of a triangle?
A: The formula for calculating the perimeter of a triangle is:
Perimeter = Side 1 + Side 2 + Side 3
Q: How do I find the perimeter of a triangle with decimal numbers?
A: To find the perimeter of a triangle with decimal numbers, you can simply add the decimal numbers together.
Q: Can I use a calculator to calculate the perimeter of a triangle?
A: Yes, you can use a calculator to calculate the perimeter of a triangle. However, make sure to enter the correct values and follow the correct order of operations.
Q: What is the difference between the perimeter and the area of a triangle?
A: The perimeter of a triangle is the sum of the lengths of its three sides, while the area of a triangle is the amount of space inside the triangle.
Q: How do I calculate the area of a triangle?
A: To calculate the area of a triangle, you need to know the base and height of the triangle. The formula for calculating the area of a triangle is:
Area = (Base × Height) / 2
Q: Can I use the perimeter to find the area of a triangle?
A: No, you cannot use the perimeter to find the area of a triangle. You need to know the base and height of the triangle to calculate its area.
Q: What is the relationship between the perimeter and the area of a triangle?
A: The perimeter and area of a triangle are related in that the perimeter is the sum of the lengths of the sides, while the area is the amount of space inside the triangle. However, there is no direct formula to calculate the area of a triangle using its perimeter.
Q: Can I use the perimeter to find the length of a side of a triangle?
A: No, you cannot use the perimeter to find the length of a side of a triangle. You need to know the lengths of the other two sides to calculate the length of the third side.
Q: How do I find the length of a side of a triangle using the perimeter?
A: To find the length of a side of a triangle using the perimeter, you need to know the lengths of the other two sides. You can use the Pythagorean theorem to calculate the length of the third side.
Q: What is the Pythagorean theorem?
A: The Pythagorean theorem is a mathematical formula that describes the relationship between the lengths of the sides of a right triangle. The formula is:
a^2 + b^2 = c^2
where a and b are the lengths of the legs of the triangle, and c is the length of the hypotenuse.
Q: Can I use the Pythagorean theorem to find the length of a side of a triangle?
A: Yes, you can use the Pythagorean theorem to find the length of a side of a triangle. However, make sure that the triangle is a right triangle, and that you know the lengths of the other two sides.
Q: What is the difference between a right triangle and a non-right triangle?
A: A right triangle is a triangle with one right angle (90 degrees), while a non-right triangle is a triangle with no right angles.
Q: Can I use the perimeter to find the length of a side of a non-right triangle?
A: No, you cannot use the perimeter to find the length of a side of a non-right triangle. You need to know the lengths of the other two sides to calculate the length of the third side.
Q: How do I find the length of a side of a non-right triangle?
A: To find the length of a side of a non-right triangle, you need to know the lengths of the other two sides. You can use the law of cosines to calculate the length of the third side.
Q: What is the law of cosines?
A: The law of cosines is a mathematical formula that describes the relationship between the lengths of the sides of a triangle. The formula is:
c^2 = a^2 + b^2 - 2ab * cos(C)
where a and b are the lengths of the legs of the triangle, c is the length of the third side, and C is the angle between the legs.
Q: Can I use the law of cosines to find the length of a side of a triangle?
A: Yes, you can use the law of cosines to find the length of a side of a triangle. However, make sure that you know the lengths of the other two sides and the angle between them.